Explain
the difference between static and dynamic systems
Answer:
Static
System:
A
system whose response or output is due to present input alone is known
as static system. The static system is also called the memoryless
system. For a static or memoryless system, the output of the system at any
instant of time (t for continuous-time system or n for discrete-time system)
depends only on the input applied at that instant of time (t or n), but not on
the past or future values of the input.
Dynamic System
A
system whose response or output depends upon the past or future inputs in
addition to the present input is called the dynamic system. The dynamic
systems are also known as memory systems. Any continuous-time dynamic
system can be described by a differential equation or any discrete-time dynamic
system by a difference equation.
An
electric circuit containing inductors and (or) capacitors is an example of
dynamic system. Also, a summer or accumulator, a delay circuit, etc. are some
examples of discrete-time dynamic systems.
Explain the difference between linear and nonlinear systems*
Linear System: A system is said to be linear if it obeys the principle of homogeneity
and principle of superposition. Or A system may have input and output.A
system is called Linear system
if it satistfied two conditions
(1)
If input is X=x1+x2
then the output must be Y=E[x1+x2]=E[x1]+E[x2]
(2)
If input is
X=a.X1+b.X2 then the output must be Y=E[a.X1+b.X2]=aE[X1]+b.E[X2] linear relationship exists between input and
output
For
example prices versus quality of petrol at filling station weight applied to a string versus its extension
Non-linear
A system is said to be a non-linear system
if it does not obey the principle of homogeneity and principle of
superposition.
Generally,
if the equation describing the system contains square or higher order terms of
input/output or product of input/output and its derivatives or a constant, the
system will be a non-linear system. Triangulation of GPS signals is an example
of non-linear system.
For
Example Input and output have non-linear relationship fare versus distance
traveled by air, land or sea
Find a linear system (write the mathematical model) that best
explain the following set of input and output variables. Input (independent
variable) = 3, 2, 4, 6 Output (dependent variable)= 4,5,9,10
Answer:
Independent
variable=3,2,4,6
Dependent variable=4,5,9,10
Function =f(y)=mx+b
Where y=dependent
variable
X=independent variable
M=stop
And can be calculated
as: m=change in Y∕change in X
B=constant
Now calculating m and b
M=change in y∕change in
x
M=1/1=0 as y is 4 and increase to 5 so change =1. 4
on this way change in x=-1
So y=mx+b
Put values 4=0(3)+b
4=0+b
B=4
Put value in functions
F(y)=mx+b
F(y)=0(3)+4
F(y)=4
So if we put 3 as input
the function returns 4 as output
Now putting value 2 in
function
M=4/2=2
Y=mx+b
5=2(2)+b
5=4+b
B=5-4=1
F(y)=mx+b
F(y)=2(2)+1
F(y)=4+1
5
And so on
Find the minimum and maximum value of the function f(x, y) = 2x
- y. We are given the constraints: 5 ≥ y ≥ 2,
1 ≤ x ≤5,
y ≤ x + 3*
Answer:
Vertixes are
V(1)=(1,2)
V(2)=(2,5)
V(3)=(5,2)
V(4)=(5,5)
V(5)=(1,5)
Putting the value in function
(1) f(1,2)=2(1)-(2)=0
(2) f(2,5)=2(2)-(5)=-1
(3) f(5,2)=2(5)-(2)=8
(4) f(5,5)=2(5)-(5)=5
(5) f(1,4)=2(1)-(4)=-2
So f(min)=-2
And f(max)=8
Explain the difference between Deterministic and
Stochastic models.*
Deterministic is that type of model in which we give
specified input and it give us a model is able to provide expected solution
The best example is
banking system
Stochastic is that of model in which we give a
specified input and it give us a model
may produce random output
The best example is
radar system Model receiving signals corrupted by noise)
Unlike deterministic models that produce the same particular
results for a particular set of inputs, stochastic models are the opposite; the
model presents data and predicts outcomes that account for certain levels of
unpredictability or randomness.